We experimentally investigate the atom-optical delta-kicked harmonic oscillator for the case of nonlinearity due to collisional interactions present in a Bose-Einstein condensate. A Bose condensate of rubidium atoms tightly confined in a static harmonic magnetic trap is exposed to a one-dimensional optical standing-wave potential that is pulsed on periodically. We focus on the quantum anti-resonance case for which the classical periodic behavior is simple and well understood. We show that after a small number of kicks the dynamics is dominated by dephasing of matter wave interference due to the finite width of the condensate's initial momentum distribution.In addition, we demonstrate that the nonlinear mean-field interaction in a typical harmonically confined Bose condensate is not sufficient to give rise to chaotic behavior. The delta-kicked rotor is an extensively investigated system in the field of classical chaos theory. During the last decade great progress has been achieved in understanding quantum dynamics of a classically chaotic system using atom-optical techniques and cold atoms. From an experimental point of view, cold atoms in optical potentials [1,2,3,4,5] provide an ideal environment to explore quantum dynamics. To date, all experimental work has focused on linear atomic systems, (see, for example, [6,7,8,9] and references therein) where the quantum dynamics is stable due to the linearity of the Schrödinger equation. In stark contrast to the chaotic behavior of classical dynamics, the linear quantum systems exhibit anti-resonance (periodic motion), dynamical localization (quasi-periodic motion) or resonant dynamics [10,11].Recently, theoretical investigations have considered how the nonlinearity due to many-body (collisional) interactions in a Bose-Einstein condensate modifies the behavior of the atom-optical kicked rotor system, providing a route to chaotic dynamics. Gardiner et al. developed a theoretical formalism to treat the one-dimensional nonlinear kicked harmonic oscillator (a particular manifestation of the generic delta-kicked rotor) using GrossPitaevskii and Liouville-type equations to describe the dynamics of a Bose-Einstein condensate, and estimated the growth rate in the number of non-condensate particles [12]. Zhang et al. investigated the generalized quantum kicked rotor by considering a periodically kicked Bose condensate confined in a ring potential for the case of quantum anti-resonance [13]. As opposed to the familiar periodic behavior exhibited by a corresponding linear system, they predicted quasi-periodic variation in energy for a weak interaction strength and chaotic behavior for strong interactions.In this work we investigate the nonlinear delta-kicked harmonic oscillator by performing experiments on BoseEinstein condensates in a harmonic potential. A Bose condensate of rubidium atoms tightly confined in a static harmonic magnetic trap is exposed to a periodically pulsed one-dimensional optical standing-wave potential. Our focus is on the particular case of quantum antireso...

We describe a new implementation of magnetic collider for investigating cold collisions between ultracold atomic clouds in different spin states, and we use this to investigate scattering involving both even and odd order partial waves. Our method relies on the axial assymetry of a double-well magnetic trap to selectively prepare the spin state in each cloud. We measure the energy dependence of s, p and d partial wave phase shifts in collisions up to 300 µK between 87 Rb atoms in the 5S 1/2 , F = 1, mF = −1 and 5S 1/2 , F = 2, mF = 1 states. 03.65.Nk, 34.10.+x, 32.80.Pj Collisions in ultracold and degenerate quantum gases play a key role in many of their interesting properties [1]. So far, investigations with ultracold atoms have been mostly concerned with s-wave scattering processes, but now nonzero partial waves play a critical role in many investigations, (see, e.g., [2]). A magnetic collider scheme for determining the contribution made by higher-order partial waves was recently implemented [3,4]. In these experiments the atoms were in the same spin state, limiting the collisions to those involving only even-order partial waves -a consequence of the particles being indistinguishable bosonic particles.In the present work, we extend our collider method to distinguishable bosons for which the scattering is fundamentally different since both odd and even angular momentum components are allowed. As in our original work [3], spin-polarized 87 Rb atoms are loaded into a magnetic double-well potential which is then transformed to a single well to initiate a collision. Here, however, one of the clouds is converted to a different spin state prior to collision making the scattering patterns crucially different. We observe the interference of s, p and d partial waves for collisions between atoms in the F = 1, m F = −1 and F = 2, m F = 1 hyperfine ground states. Despite the complexity of the three-wave interference, we successfully determine the three partial wave phase shifts for energies up to 300 µK as measured in units of the Boltzmann constant k B .The angular dependence of the two-body scattering problem is described by the complex scattering amplitude f (θ) [6]. Using the partial wave expansion, this is expressed as f (θ) = 1 2ik ∞ ℓ=0 (2ℓ + 1)(e 2iη ℓ − 1)P ℓ (cos θ), where P ℓ is the ℓ th order Legendre polynomial and η ℓ are the partial wave phase shifts which depend on the scattering potential and relative wave vector k of the colliding atom pair. For the range of energies we focus on here, only the first three partial waves ℓ = 0, 1, 2 contribute [7]. In this case the differential crosssection dσ/dΩ = |f (θ)| 2 is given by dσ dΩ = 1 k 2 {sin 2 η 0 + 9 sin 2 η 1 cos 2 θ + 25 4 sin 2 η 2 (3 cos 2 θ − 1) 2 + 6 sin η 0 sin η 1 cos(η 0 − η 1 ) cos θ + 5 sin η 0 sin η 2 cos(η 0 − η 2 )(3 cos 2 θ − 1) + 15 sin η 1 sin η 2 cos(η 1 − η 2 )(3 cos 2 θ − 1) cos θ}.Because of the orthogonality and completeness of the Legendre polynomials, a fit of an interference expression in the form Eq.(1) to a measured angular distr...

We present a scheme for rapidly loading a Bose-Einstein condensate into a single Bloch state of a weak optical lattice at a quasi-momentum of q =hk. Rabi cycling of the Bose condensate between momentum states is modified by a phase shift applied to the lattice. By appropriately choosing the magnitude and timing of the phase shift, we demonstrate nearly perfect loading of the lattice ground state, the signature of which is an abrupt halt to the Rabi cycling.PACS numbers: 03.75. Lm, 32.80.Qk Recent experiments involving the manipulation of Bose-Einstein condensates (BECs) [1,2,3] in optical lattices highlight some of the remarkable features of quantum states of matter. The first experiment involving a Bose condensate and an optical lattice was performed by Anderson and Kasevich [4] observing the interference of atomic de Broglie waves tunneling through a lattice due to gravity. Optical lattices at the Bragg condition have been used to demonstrate a coherent beam splitter for de Broglie waves [5] and to make spectroscopic measurements of condensate momentum distributions [6]. A diverse range of other experiments has been performed using BECs in optical lattices [7,8,9,10,11,12,13,14], involving a wide variety of parameters and techniques. One reason for this strong interest in optical lattices is their potential application in quantum information processing [15,16,17], where precise control and negligible decoherence are essential. For use in quantum computing the condensate must first be loaded into the ground state of the lattice. This is typically done by adiabatically increasing the lattice depth (see, for example, Refs. [11, 14]) or evaporative cooling in a hybrid trap [18]. However, for the case where the quasi-momentum q approaches the boundary of the first Brillouin zone (at q = ±hk, where k = 2π/λ is the lattice wave-vector), the adiabatic loading method fails due to the initial degeneracy of the Bloch bands.In this paper we report a new scheme for rapid (nonadiabatic) loading into the ground state of an optical lattice at q =hk. A Bose condensate is placed in a weak moving lattice which induces Rabi cycling between two momentum states, 0 and 2hk, via Bragg scattering [19]. We show that by simply "jumping" the phase of the periodic standing wave potential after a 3π/2 pulse, we are able to transfer the entire population to the lattice ground state. We present a convenient geometrical representation (using the Bloch sphere [20]) which is a useful tool in predicting the outcome of our two-state manipulations. Our atom-optical scheme is adapted from the methods developed by Hartman and Hahn [21] The potential of a one-dimensional optical lattice formed by two counterpropagating laser beams is given bywhere V 0 is the lattice depth and δ is the frequency difference between the two beams. A Bose-Einstein condensate suddenly loaded into such a potential can be described in terms of Bloch eigenstates, which are a superposition of plane-wave states separated in momentum space by 2hk. When loading into a wea...

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We present detailed instructions for the construction of a pyramidal-style laser cooling and trapping apparatus. This scheme requires only a single beam, rather than the three pairs of orthogonal beams of the standard magneto-optical trap, which greatly simplifies the geometry and substantially reduces the cost. The trap is based largely on low-cost commercially available items and is simple to construct. It is remarkably insensitive to alignment and reliable to operate. Using a single laser beam with an intensity of 1.3 mW/cm2 we cool and trap more than 4 million rubidium atoms.